A defect in a semi-conductor wafer can be classified as a defect of interest (DOI), which could impact utility of the wafer, or a nuisance defect, which can be effectively ignored. In general, a defect closer to the surface of a wafer is more likely to be a DOI. As the vertical dimensions of semi-conductor devices increase, for example as in tri-gate transistors and 3-D NAND memories, it becomes increasing important to accurately determine defect depths, in particular, to ascertain whether a defect is near the top/surface of the wafer or deeper in the wafer.
FIG. 12 is a pictorial representation of light intensity used in a prior art method for determining a depth of a defect in a semi-conductor wafer. In FIG. 12 a color scale of intensities 6 (red—lowest intensity) to 20 (purple—greatest intensity) is shown on the right-hand side. It is known to detect a defect in a semi-conductor wafer using optical means. In terms of optical detection, a defect is characterized by having light scatter different from surrounding structure and can be a particle, a gap, or a missing or misshaped pattern. It is known to illuminate a wafer including one or more defects with light free of a spiral wavefront or orbital angular momentum, collect the light scattered and reflected by the wafer, and generate an image. As shown in FIG. 12, the image includes respective areas 800 of varying intensity. A defect is generally identified by an area of differing intensity, and a depth is estimated according to the relative intensity of the area. In FIG. 12, areas 802A-F are associated with defects 130A-F, respectively, described below for FIG. 4. The image is referenced to a focal plane set at a specific distance, for example, as a z position of interest, such as the surface of the wafer. However, it is extremely difficult to differentiate between an intensity associated with a defect at the focal plane and a defect close to the focal plane. Further, the type of defect (size or optical characteristics) can influence the intensity independently of the depth of the defect. For example, a larger defect at a distance from the focal plane can mimic a smaller defect at the focal plane. It is extremely difficult to ascertain how much of a particular intensity is due to the depth of a defect and how much is due to the type of the defect.